This paper is an elaboration of methods of interpolation and approximation of functions. It gives a brief description of key terms: interpolation, approximation, Lagrange's and Newton's interpolation polynomial, Least-Squares method and Spline interpolation. Each method is described by example, with the chart that best approximates the function on a given discrete set of points. Analysed data and method comparison give an insight in which method is more accurate depending on given parameters. The problem that occurs with interpolation by these methods is a sudden change of function. In that case it is necessary to reduce the area of consideration or use, for example interpolation spline right in between or around the points that oscillate the most. The given results do not enable us to single out one general procedure that applies to all cases. Each case requires an individual analysis, dissipation points analysis and selection of the best method for the specific case.